• Journal of Applied Reliability
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• v.14 no.2
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• pp.103-107
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• 2014

An algorithm to get network reliability, where each link has probability of fuzzy number, is proposed. Decomposition method and fuzzy numbers arithmetic are applied to the algorithm. Pivot link is chosen one by one from start node recursively at time of decomposition, and arithmetic of fuzzy complementary numbers is included at the same time. No criteria of pivot link selection and the recursive calculation make the algorithm simple.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.93-101
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• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.1-4
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• 2002

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication) and the relationship between entropy and information energy. It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. Moreover, the information energy variation on the fuzzy numbers is also discussed. The results generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.231-236
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• 2003

Recently, Oussalah 〔Fuzzy Sets and Systems 128(2002) 247-260〕 investigated some theoretical results about some invariance properties concerning the relationships between the defuzzification outcomes and the arithmetic of fuzzy numbers. But, in this note we introduce some explicit calculations of the resulting fuzzy set or possibility distribution when the matter is the determination of the defuzzified value pertaining to the result of some manipulation of fuzzy quantities under t-norm based fuzzy arithmetic operations.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.754-758
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• 2005

There have been several tipical methods being used tomeasure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. Recently, Wang and Chiu [FSS103(1999) 443-455] and Pedrycz [FSS 64(1994) 21-30] showed the relationship(addition, subtraction, multiplication) between the entropies of the resultant fuzzy number and the original fuzzy numbers of same type. In this paper, using Lebesgue-Stieltjes integral, we generalize results of Wang and Chiu [FSS 103(1999) 443-455] concerning entropy arithmetic operations without the condition of same types of fuzzy numbers. And using this results and trade-off relationship between information energy and entropy, we study more properties of information energy of fuzzy numbers.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy Quantities based on the extension principle suggested by Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.170-174
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• 2008

The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2876-2878
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• 1999

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication). It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. This paper generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.